[Doc] Add AI Badgr framework integration documentation

docs/deployment/frameworks/aibadgr.md

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+# AI Badgr
+
+[AI Badgr](https://aibadgr.com) is a budget-focused, OpenAI-compatible LLM provider offering tier-based model access.
+
+AI Badgr can connect to vLLM as a backend to serve local models through its OpenAI-compatible API interface.
+
+## Prerequisites
+
+Set up the vLLM environment:
+
+```bash
+pip install vllm
+```
+
+## Deploy
+
+### Using vLLM as AI Badgr's Backend
+
+1. Start the vLLM server with a supported chat completion model, e.g.:
+
+    ```bash
+    vllm serve meta-llama/Llama-3.2-3B-Instruct --host 0.0.0.0 --port 8000
+    ```
+
+2. Configure AI Badgr to point to your vLLM endpoint:
+
+    - **Base URL**: `http://{your-vllm-host}:8000/v1`
+    - **API Key**: Use any non-empty string (vLLM doesn't require authentication by default)
+    - **Model**: Use the model name from your vLLM deployment (e.g., `meta-llama/Llama-3.2-3B-Instruct`)
+
+### Connecting to AI Badgr's API
+
+If you want to connect to AI Badgr's hosted service instead, you can use any OpenAI-compatible client:
+
+```python
+import os
+from openai import OpenAI
+
+# AI Badgr configuration using environment variables
+client = OpenAI(
+    base_url=os.getenv("AIBADGR_BASE_URL", "https://aibadgr.com/api/v1"),
+    api_key=os.getenv("AIBADGR_API_KEY")
+)
+
+# AI Badgr uses tier-based model names
+# Tier models: basic, normal, premium (recommended)
+response = client.chat.completions.create(
+    model="premium",  # or "normal", "basic"
+    messages=[
+        {"role": "user", "content": "Hello, how are you?"}
+    ],
+    temperature=0.7,
+    max_tokens=150
+)
+
+print(response.choices[0].message.content)
+```
+
+### Environment Variables
+
+When using AI Badgr's hosted service, you can set these environment variables:
+
+- `AIBADGR_API_KEY`: Your AI Badgr API key
+- `AIBADGR_BASE_URL`: Base URL for AI Badgr API (default: `https://aibadgr.com/api/v1`)
+
+!!! note "Budget/Utility Provider"
+    AI Badgr is positioned as a budget-focused utility provider. The tier-based pricing model (basic/normal/premium) allows cost optimization based on your use case.
+
+## Model Tiers
+
+AI Badgr offers tier-based model access:
+
+- **basic**: Budget-tier models for simple tasks
+- **normal**: Balanced performance and cost
+- **premium**: Recommended default for most applications
+
+Advanced users can also use specific model names for reproducibility or when they need to target exact model versions:
+
+- `phi-3-mini` (maps to basic tier)
+- `mistral-7b` (maps to normal tier)
+- `llama3-8b-instruct` (maps to premium tier)
+
+OpenAI model names (e.g., `gpt-3.5-turbo`) are also accepted and mapped automatically by AI Badgr to equivalent tier models.